Calculus question and answers for August 20, 2023
- Q your answer No x Decimal answers MUST be correct to THRE decimal places Question 8 log 3x 1 2 1 pts
- Q During flu season, the number of people that contract the flu virus at any time increases at a rate proportional to the number of people that contract the flu virus...
- Q If sin(?)=-2/5 and is in the 3rd quadrant, find cos(?)
- Q A tank of water in the shape of an inverted cone (i.e. circular base on top) is leaking water a constant rage of 1 ft3/min. The base radius of the...
- Q Consider the set of all rectangles that lie in the first quadrant, have one edge along the posi- tive x-axis, one corner at the origin, and the diagonally opposite corner...
- Q Find the domain of the following rational function. R(x) =8(x-4x-21)/9(x-49) Select the correct choice below and fill in any answer boxes within your choice. A. The domain of R(x) is...
- Q Find the real solutions of the following equation.Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A. The solution set is.B. The solution...
- Q Solve the equation in the real number system.x4-2x3 +8x-32x-128=0Select the correct choice below and fill in any answer boxes in your choice.A. The real solutions of the equation are x...
- Q Let f(x, y) 6x 2x - 3y + 6ay. This function has critical points at (0, 0) and (3, 3). Determine if these points are a localmaximum, local minimum, or...
- Q Find the intercepts of the graph of the equation y = x-1/x-4Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A. The intercept(s)...
- Q All but one of the functions is differentiable for all real values of x. Which function isnot differentiable for at least one real value of x?f(x)=x +1g(x) = 1/x +1h(x)...
- Q a. Determine the coordinates of the point on the graph of f(x)=-x+3x+1 where thetangent line is perpendicular to the line y=x+2.b. Write the equation of the tangent line at this...
- Q In this question, you should determine the asymptotes andUse calculus and algebraic methods to do a complete analysis (i.e., intercepts, critical points, intervals ofincrease and decrease, points of inflection, intervals...
- Q Andrea plots(-5,-2)on the polar plane.How does she proceed?Drag a phrase to each box to correctly complete the statements.Andrea first determines which line the angle of rotation places the point on....
- Q Problem 6. (10 points) (Related Rates) Suppose you have an ice cream cone with radius 4cm and height 12 cm with some melted boysenberry ice cream in it. The ice...
- Q Problem 7. (10 points) (Optimization) Consider the function f that is given by2/x2+1Of all lines tangent to the graph of f, find the value of a where the tangent line...
- Q Assume that the rate of evaporation for water is proportional to the initial amount of water in a bowl. Jill places 1 cup and 8 ounces of water outside and...
- Q 2. In this question, you should determine the asymptotes and Use calculus and algebraic methods to do a complete analysis (i.e., intercepts, critical points, intervals of increase and decrease, points...
- Q Consider the curve e^xy + 3x + y = 65.a. Find the equation of the tangent line at the point (0,8).b. There are two points on the curve with x-coordinate...
- Q Let S = {r: r is a positive number such that ork/k! converges absolutely for || <r}. Which of the following statement is true?(a) S is empty.(b) S is nonempty...
- Q A lighthouse is located 215 feet from the nearest point P on a straight shoreline. The revolving beacon in thelighthouse makes one revolution every 6 seconds. Find the rate at...
- Q A highway and a railway cross at and angle of 22 degrees. A passenger train is approaching the intersection at74 miles per hour while a car is approaching the intersection...
- Q A 5 foot tall man jogs at a rate of 23 feet per second toward a lamppost that is 19 feet tall.Determine the rate of change of the tip of...
- Q Solve for x where T ? x ? 2?sinx - cosxcosx[?]T= 0=?
- Q Perform the following operation,and write the answer in scientificnotation with the correct numberof significant figures.0.00851.3= [?] x 10
- Q Solve for x by factoring where0?x?T.tanx - tan x = 00, [2] T7Enter the next smallest value.
- Q Let f(x) = - 3 cos x for 0 ? x ? ?.Determine the derivative of f- at x =(1-)-(-3?) - (23?32
- Q Corn is falling off a conveyor belt onto a conical pile at the rate of 10 cubic feet per minute. The diameter ofthe base of the pile is 4 times...
- Q Perform the mathematical operation and round the answer to the appropriate number of significant figures. 24.32 x 0.010 = [?
- Q The radius of a sphere is increasing at a rate of 2 centimeters per hour. Determine the rate of change of thesphere's surface area when the radius is 25 centimeters.square...
- Q The radius of a circle is increasing at a rate of 10 inches per minute. Determine the rate of change of thecircle's area when the radius is 41 inches.square inches...
- Q A 6 foot tall woman walks at a rate of 6 feer per second toward a lamppost that is 15 feet tall.Determine the rate of change of the tip of...
- Q Let h(x) = - 2x - 3Determine the derivative of h- at x = 5.(h-) '(-5) =
- Q The radius of a sphere is increasing at a rate of 3 centimeters per hour. Determine the rate of change of thesphere's volume when the radius is 16 centimeters.cubic centimeters...
- Q The point P(3, -3) lies on the curve y =(a) If Q is the point x,(i) 2.9MpQ(ii) 2.99MpQ =E(iii) 2.999mpQ(iv) 2.9999MPQ(v) 3.1MPQ(vi) 3.01MPQ=(vii), 3.001MPQ=3(x?___-).(viii) 3.0001m =PQ32-xfind the slope of the...
- Q Suppose x and y are both differentiable functions of t andx + y = c5where c is a constant.Determinedydt=dydt"givendxdt233, x=-3, and y = 1.
- Q Air traffic control detects two airplanes at the same altitude converging on a single point as they fly at rightangles to each other. One plane is 152 miles away from...
- Q Let g(w) = arctan( - 6w)Determine the derivative of g.g'(w) ==Determine the slope of g at w = 9.g'(9) =
- Q Suppose both f and f-1 are differentiable functions such that. f(7) = 8 f'(7) =79Determine the equation of the tangent line of f at x = 8. Report the solution...
- Q Let g(x) = (x - 8x ++3)Determine the equation of the tangent line to g at x = 7. Report the solution using slope-intercept form.
- Q Let f(x) =Determine the derivative of f.f'(x) =Determine the slope of fat x = 3.f'(3) ==-3 cot(8x)
- Q Let h(z)arccot ( 122 +212)-Determine the value(s) of z, if any, for which h has a horizontal tangent line.Oh has a horizontal tangent line at z =Oh has no horizontal...
- Q For the given function, (a) find the slope of the tangent line to the graph at the given point;(b) find the equation of the tangent line.9h(x) = -atx=7X(a) The slope...
- Q Suppose the line y = 5x - 9 is tangent to the curve y = f(x) when x = 3. If Newton's method is used to locate a root of...
- Q Assume that .x, y, z are positive. Use Lagrange multipliers to find the maximum of the function f(x.y.z)= e^xyz subject to the constraint x + y + = 9.
- Q Consider the following function.f(x) =x2-49(a) Find the critical numbers of f. (Enter your answers as a comma-separated list.)X =(b) Find the open intervals on which the function is increasing or...
- Q Find the rate of change of y with respect to x at the indicated value of x.y csc(x) - 6 cos(x); x=?/6y'=
- Q Consider the following function.x2x - 49(a) Find the critical numbers of f. (Enter your answers as a comma-separated list.)x = (0,0)=(b) Find the open intervals on which the function is...
- Q Consider the function below.f(x) = -4x + 24x + 2(a) Find the critical numbers of f. (Enter your answers as a comma-separated list.)X =(b) Find the open intervals on which...
- Q Consider the function on the interval (0, 2).f(x) = sin(x) cos(x) + 2(a) Find the open interval(s) on which the function is increasing or decreasing. (Enter your answers using interval...
- Q Consider the following function.f(x) = 5x +1x(a) Find the critical numbers of f. (Enter your answers as a comma-separated list.)(b) Find the open intervals on which the function is increasing...
- Q Consider the following function.f(x) = (5x)(x + 1)(a) Find the critical numbers of f. (Enter your answers as a comma-separated list.)X =(b) Find the open intervals on which the function...
- Q No, because p cannot be negativeP = 84Yes, because each value of a corresponds to exactly one value of pOYes, because the relation defines p in terms of sO No,...
- Q Consider the following function.f(x) = x - 32x + 2(a) Find the critical numbers of f. (Enter your answers as a comma-separated list.)X =(b) Find the open intervals on which...
- Q Consider the function on the interval (0, 2).f(x) = sin x + cos x(a) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using...
- Q Simplify.sin x sec x - sin x csc x[?]x - [ ]
- Q If the rate of change of T is proportional to (30+ T), where T > -30. If T(0) = 4, andT(2) = 6, find T(5).
- Q Consider the measurements shown. The most precise value is highlighted for each measurement. 9.3478 m + 2.73 m =What place value must the answer be reported to?1. ones place2. tenths...
- Q Find an equation for a positive sine function having an amplitude of 1/4, a period of 4?, and a horizontal shift of 4? to the right. y = __/__ sin...
- Q Find the average value gave of the function g on the given interval.g(t) = 2/(1 + t2')[0, 7]
- Q Round to 2 significantfigures.42.598
- Q An open-top rectangular box is being constructed to hold a volume of 350 in. The base of the box is madefrom a material costing 6 cents/in. The front of the...
- Q Question 4 Given two vectors a = (1, 2, 1) and 6 = (4, 2k + 1, k) :a) Determine the value of k that makes them perpendicularb) Determine the...
- Q Round to 4 significant figures.35.5450
- Q correspondsbetweenIf y = cos x, what x-valueto a y-value ofand 2??
- Q Graph the polar equation. Identify the name of the shape.# 40 r 4 sin(50)a) Identify the shape: rose curveb) Identify the number of petals: 20 Xc) Identify the length of...
- Q The volume of a cone of radius r and height h is given by V-rh.trh. If the radius and the heightV=-? centimeter per second, at what rate, in cubic centimeters...
- Q The graph of a twice-differentiable function f is shown in the figure above. Which of thefollowing is true?(A) f(1)<f'(1)<" (1)(B) f(1)<f'(1)<f'(1)(C) f'(1)<f(1)<^(1)(D) f'(1)<f(1)<f'(1)(E) f'(1)<f'(1)<(1)
- Q Which sound device does theauthor use in the underlinedwords from the poem?In sunshine and in shadow,Had journeyed long,Singing a song,In search of Eldorado.A. repetition (repeated words)B. end rhyme (repeated rhyme...
- Q Let P (x) represent the population (in thousands) in a region a years since year1950.Use function notation to represent that the population is 540,000 in the year1978.OP(28) = 540O P(1978)...
- Q 65. A man starts walking from home and walks 3 miles at 20 north of west, then 5 miles at 10 west of south,then 4 miles at 15 north of...
- Q Suppose y sin x.What is the x-value between2? and 47corresponding to a y-value of -1?
- Q |Convert the given polarcoordinates into rectangularcoordinates.(-2, ?) = ([?], [])Enter
- Q Let y = 5x.Find the change in y, ?y when x = 2 and ?x = 0.2Find the differential dy when x = 2 and dx=0.2
- Q Let y = tan(5x + 8).Find the differential dy when x = 4 and dx = 0.2Find the differential dy when x = 4 and dx = 0.4
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